Rewrite as a simplified fraction. ${1.\overline{63} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 163.6363...\\ 1x &= 1.6363...\end{align*}}$ Subtracting the two equations, we have: ${99x = 162}$ ${x = \dfrac{162}{99}} $ ${x = \dfrac{18}{11}} \text{or} {1 \dfrac{7}{11}}$